# Doppler spectral moments

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− | <div class="definition"><div class="short_definition">Statistical moments of Doppler frequency or [[Doppler velocity]], regarding these quantities as continuously distributed [[random]] variables with a [[probability density function]] equal to the normalized [[Doppler spectrum]].</div><br/> <div class="paragraph">If ''S''(''f'') denotes the Doppler spectrum as a function of Doppler frequency ''f,'' the ''n''th [[moment]] is defined by <div class="display-formula"><blockquote>[[File:ams2001glos-De39.gif|link=|center|ams2001glos-De39]]</blockquote></div> where the denominator normalizes the Doppler spectrum to unit area. The ''n''th moment in terms of Doppler velocity is related to that in terms of [[frequency]] by <div class="display-formula"><blockquote>[[File:ams2001glos-De40.gif|link=|center|ams2001glos-De40]]</blockquote></div> where λ is the radar [[wavelength]]. The first [[moment]] of [[velocity]] is called the [[mean Doppler velocity]] and the second [[central moment]] is called the Doppler velocity [[variance]]. The [[Doppler spread]] usually denotes the square root of the Doppler velocity variance. <br/>''See'' [[Doppler frequency shift]].</div><br/> </div> | + | <div class="definition"><div class="short_definition">Statistical moments of Doppler frequency or [[Doppler velocity]], regarding these quantities as continuously distributed [[random]] variables with a [[probability density function|probability density function]] equal to the normalized [[Doppler spectrum]].</div><br/> <div class="paragraph">If ''S''(''f'') denotes the Doppler spectrum as a function of Doppler frequency ''f,'' the ''n''th [[moment]] is defined by <div class="display-formula"><blockquote>[[File:ams2001glos-De39.gif|link=|center|ams2001glos-De39]]</blockquote></div> where the denominator normalizes the Doppler spectrum to unit area. The ''n''th moment in terms of Doppler velocity is related to that in terms of [[frequency]] by <div class="display-formula"><blockquote>[[File:ams2001glos-De40.gif|link=|center|ams2001glos-De40]]</blockquote></div> where λ is the radar [[wavelength]]. The first [[moment]] of [[velocity]] is called the [[mean Doppler velocity|mean Doppler velocity]] and the second [[central moment]] is called the Doppler velocity [[variance]]. The [[Doppler spread|Doppler spread]] usually denotes the square root of the Doppler velocity variance. <br/>''See'' [[Doppler frequency shift|Doppler frequency shift]].</div><br/> </div> |

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## Latest revision as of 17:49, 25 April 2012

## [edit] Doppler spectral moments

Statistical moments of Doppler frequency or Doppler velocity, regarding these quantities as continuously distributed random variables with a probability density function equal to the normalized Doppler spectrum.

If where the denominator normalizes the Doppler spectrum to unit area. The where λ is the radar wavelength. The first moment of velocity is called the mean Doppler velocity and the second central moment is called the Doppler velocity variance. The Doppler spread usually denotes the square root of the Doppler velocity variance.

*S*(*f*) denotes the Doppler spectrum as a function of Doppler frequency*f,*the*n*th moment is defined by*n*th moment in terms of Doppler velocity is related to that in terms of frequency by*See*Doppler frequency shift.